Nuclear Norm Regularized Estimation of Panel Regression Models

10/25/2018
by   Hyungsik Roger Moon, et al.
0

In this paper we investigate panel regression models with interactive fixed effects. We propose two new estimation methods that are based on minimizing convex objective functions. The first method minimizes the sum of squared residuals with a nuclear (trace) norm regularization. The second method minimizes the nuclear norm of the residuals. We establish the consistency of the two resulting estimators. Those estimators have a very important computational advantage compared to the existing least squares (LS) estimator, in that they are defined as minimizers of a convex objective function. In addition, the nuclear norm penalization helps to resolve a potential identification problem for interactive fixed effect models, in particular when the regressors are low-rank and the number of the factors is unknown. We also show how to construct estimators that are asymptotically equivalent to the least squares (LS) estimator in Bai (2009) and Moon and Weidner (2017) by using our nuclear norm regularized or minimized estimators as initial values for a finite number of LS minimizing iteration steps. This iteration avoids any non-convex minimization, while the original LS estimation problem is generally non-convex, and can have multiple local minima.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
04/19/2019

Square-root nuclear norm penalized estimator for panel data models with approximately low-rank unobserved heterogeneity

This paper considers a nuclear norm penalized estimator for panel data m...
research
06/13/2020

Low-Rank Factorization for Rank Minimization with Nonconvex Regularizers

Rank minimization is of interest in machine learning applications such a...
research
09/14/2018

Efficient Rank Minimization via Solving Non-convexPenalties by Iterative Shrinkage-Thresholding Algorithm

Rank minimization (RM) is a wildly investigated task of finding solution...
research
04/26/2018

GEP-MSCRA for computing the group zero-norm regularized least squares estimator

This paper concerns with the group zero-norm regularized least squares e...
research
06/30/2017

Nuclear penalized multinomial regression with an application to predicting at bat outcomes in baseball

We propose the nuclear norm penalty as an alternative to the ridge penal...
research
11/06/2018

Sparse and Smooth Signal Estimation: Convexification of L0 Formulations

Signal estimation problems with smoothness and sparsity priors can be na...
research
03/19/2022

New algorithms for computing the least trimmed squares estimator

Instead of minimizing the sum of all n squared residuals as the classica...

Please sign up or login with your details

Forgot password? Click here to reset